A search for B-(s)(0) -> K-S (0) K*(892)(0) decays is performed using pp collision data, corresponding to an integrated luminosity of 1.0 fb(-1), collected with the LHCb detector at a centre-of-mass energy of 7 TeV. The B-s (0) -> (KSK)-K-0*(892)(0) decay is observed for the first time, with a significance of 7.1 standard deviations. The branching fraction is measured to be B(B-s(0) -> (K) over bar K-0*(892)(0)) + B(B-s(0) -> K-0(K) over bar*(892)(0)) = (16.4 +/- 3.4 +/- 2.3) x10(-6), where the first uncertainty is statistical and the second is systematic. No evidence is found for the decay B-0 ->(KSK)-K-0*(892)(0) and an upper limit is set on the branching fraction, B(B-0 -> (K) over bar K-0*(892)(0)) + B(B-0 -> K-0(K) over bar*(892)(0)) < 0.96 x 10(-6) , at 90 % confidence level. All results are consistent with Standard Model predictions.
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